# The centre of the ellipse 3x^2 + 4y^2 – 12x – 8y + 4 = 0 is

Q: The centre of the ellipse 3x2 + 4y2 – 12x – 8y + 4 = 0 is

(A) (1, 1)

(B) (2, 1)

(C) (3, 1)

(D) none of these

Sol. The equation of the ellipse can be written as

3 (x2 – 4x + 4) + 4 (y2 – 2y + 1) = 12

⇒ $\large \frac{(x-2)^2}{4} + \frac{(y-1)^2}{3} = 1$

⇒ (2, 1) is the centre.